The traditional Becker/Arrow style model of discrimination depicts majority and minority and workers as perfectly substitutable inputs, implying that all workers have the same job assignment. The model is only appropriate for determining whether pay differences between, for example, whites and non-whites doing job assignment A are attributable to prejudice ('within-assignment discrimination'); It is inappropriate, however, for determining whether pay differences between whites in job assignment A and non-whites in job assignment B reflect discriminatory behaviour ('cross-assignment discrimination'). We test the model of such cross assignment discrimination developed by Bodvarsson and Sessions (2011) using data on Major League Baseball hitters and pitchers for four different seasons during the 1990s, a decade during which monopsony power fell. We find strong evidence of ceteris paribus racial pay differences between hitters and pitchers, as well as evidence that cross-assignment discrimination varies with labour market structure.